Related papers: Modeling clustered non-stationary Poisson processe…
Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…
A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…
Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
The problem of sequential change diagnosis is considered, where observations are obtained on-line, an abrupt change occurs in their distribution, and the goal is to quickly detect the change and accurately identify the post-change…
Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…
Overdispersed count data are modelled with likelihood and non-likelihood approaches. Likelihood approaches include the Poisson mixtures with three distributions, the gamma, the lognormal, and the inverse Gaussian distributions.…
Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…
We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
We consider a cascade model of $N$ different processors performing a distributed parallel simulation. The main goal of the study is to show that the long-time dynamics of the system has a cluster behavior. To attack this problem we combine…
The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…